Make parent-owned sub-agent threads read-only in the TUI (#33841)

## Why

Multi-agent V2 spawned threads are controlled by their parent and reject direct
app-server input. The TUI should expose that ownership instead of presenting an
input flow that the server will reject.

## What changed

- Add the experimental `Thread.canAcceptDirectInput` capability for loaded
  threads and populate it from the same policy used to validate `turn/start`
  and `turn/steer`. Stored, unloaded threads report `null`.
- Carry the capability through TUI thread discovery, selection, startup, and
  resume flows, with a compatibility fallback for older app servers.
- Present parent-owned threads as view-only, preserve drafts and queued input,
  block agent-directed commands and settings shortcuts, and keep local
  navigation and inspection commands available.

## Testing

- Cover V1 writable and V2 view-only spawned threads through selection and
  resume.
- Cover composer submission paths, queued and initial input preservation,
  allowed navigation commands, settings shortcuts, and the view-only UI.

GitOrigin-RevId: 495ad051249e5577fb0b0c1cc8c40a0998d04918

codex-rs/app-server-protocol/src/protocol/common.rs

@@ -2639,6 +2639,7 @@ mod tests {
                     cwd: cwd.clone(),
                     cli_version: "0.0.0".to_string(),
                     source: v2::SessionSource::Exec,
+                    can_accept_direct_input: None,
                     thread_source: None,
                     agent_nickname: None,
                     agent_role: None,
@@ -2692,6 +2693,7 @@ mod tests {
                         "cwd": absolute_path_string("tmp"),
                         "cliVersion": "0.0.0",
                         "source": "exec",
+                        "canAcceptDirectInput": null,
                         "threadSource": null,
                         "agentNickname": null,
                         "agentRole": null,

codex-rs/app-server-protocol/src/protocol/v2/tests.rs

@@ -195,6 +195,7 @@ fn thread_resume_response_round_trips_initial_turns_page() {
             cwd: absolute_path("tmp"),
             cli_version: "0.0.0".to_string(),
             source: SessionSource::Exec,
+            can_accept_direct_input: None,
             thread_source: None,
             agent_nickname: None,
             agent_role: None,

codex-rs/app-server-protocol/src/protocol/v2/thread_data.rs

@@ -208,6 +208,10 @@ pub struct Thread {
     pub cli_version: String,
     /// Origin of the thread (CLI, VSCode, codex exec, codex app-server, etc.).
     pub source: SessionSource,
+    /// Whether the app server accepts direct turn input for this loaded thread.
+    /// `None` means the capability is unavailable, such as for an unloaded stored thread.
+    #[experimental("thread.canAcceptDirectInput")]
+    pub can_accept_direct_input: Option<bool>,
     /// Optional analytics source classification for this thread.
     pub thread_source: Option<ThreadSource>,
     /// Optional random unique nickname assigned to an AgentControl-spawned sub-agent.